Bounds for the gradient of the transition kernel for elliptic operators with unbounded diffusion, drift and potential term

TL;DR

This paper establishes global Sobolev regularity and pointwise bounds for the gradient of transition densities of second order differential operators with unbounded coefficients in Euclidean space.

Contribution

It provides new theoretical bounds and regularity results for transition kernels of elliptic operators with unbounded diffusion, drift, and potential terms.

Findings

Proved global Sobolev regularity of transition densities.

Derived pointwise upper bounds for the gradient of transition densities.

Extended analysis to operators with unbounded coefficients.

Abstract

We prove global Sobolev regularity and pointwise upper bounds for the gradient of transition densities associated with second order differential operators in $\mathbb{R}^d$ with unbounded diffusion, drift and potential terms.